Learning the Parameters of Global Constraints Using Branch-and-Bound

Picard-Cantin, Émilie; Bouchard, Mathieu; Quimper, Claude-Guy; Sweeney, Jason Pierre

doi:10.1007/978-3-319-66158-2_33

Cited by 5 publications

(2 citation statements)

References 21 publications

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“…This operator is efficient when it is a question of verifying a precise and unique constraint, but not very efficient when it is a question of searching for the parameters of a constraint such that the resulting constraint is satisfied by a set of solutions. Finding the parameters of a global constraint so that it is satisfied by a set of solutions is a recurrent problem at present ( [11], [12], [8], [2], [4]). To solve this problem we propose to work with M DD(S) which we enrich by introducing the notion of node properties.…”

Section: Introductionmentioning

confidence: 99%

Checking Constraint Satisfaction

Jung

Régin

2021

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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We address the problem of verifying a constraint by a set of solutions S. This problem is present in almost all systems aiming at learning or acquiring constraints or constraint parameters. We propose an original approach based on MDDs. Indeed, the set of solutions can be represented by the MDD denoted by M DDS . Checking whether S satisfies a given constraint C can be done using M DD(C), the MDD that contains the set of solutions of C, and by searching if the intersection between M DD(S) and M DD(C) is equal to M DD(S). This step is equivalent to searching whether M DD(S) is included in M DD(C). Thus, we give an inclusion algorithm to speed up these calculations. Then, we generalize this approach for the computation of global constraint parameters satisfying C. Next, we introduce the notion of properties on the MDD nodes and define a new algorithm allowing to compute in only one step the set of parameters we are looking for. Finally, we present experimental results showing the interest of our approach.

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Section: Introductionmentioning

confidence: 99%

Checking Constraint Satisfaction

Jung

Régin

2021

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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“…profit values for items in the knapsack problem, are estimated with machine learning rather than given precisely. In terms of modeling, constraint acquisition [1] uses machine learning techniques to learn structural constraints from data, while other works are concerned with finding the most likely parameters of given hard constraints [20]. Closely related, as predictions are used in the objective, is the emerging topic of constructive machine learning [22,7], where the goal is to learn to synthesize structured objects from data, e.g.…”

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confidence: 99%

An Investigation into Prediction + Optimisation for the Knapsack Problem

Demirović

Stuckey

Bailey

et al. 2019

Lecture Notes in Computer Science

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We study a prediction+optimisation formulation of the knapsack problem. The goal is to predict the profits of knapsack items based on historical data, and afterwards use these predictions to solve the knapsack. The key is that the item profits are not known beforehand and thus must be estimated, but the quality of the solution is evaluated with respect to the true profits. We formalise the problem, the goal of minimising expected regret and the learning problem, and investigate different machine learning approaches that are suitable for the optimisation problem. Recent methods for linear programs have incorporated the linear relaxation directly into the loss function. In contrast, we consider less intrusive techniques of changing the loss function, such as standard and multi-output regression, and learning-to-rank methods. We empirically compare the approaches on real-life energy price data and synthetic benchmarks, and investigate the merits of the different approaches.Combinatorial optimisation is crucial in today's society and used throughout many industries. In this paper, we work with the fundamental knapsack problem, which has been studied for over a century and is well understood [17,9]. It is studied in fields such as combinatorics, computer science, complexity theory, cryptography, and applied mathematics. It has numerous applications, including resource allocation problems where the aim is to select as many resources as possible under given financial constraints. The knapsack problem is NP-hard, though highly efficient solution methods exist for reasonably sized instances [9].In traditional optimisation, it is assumed that all parameters, e.g. the profits and weights in a knapsack, are precisely known beforehand. In practice, these are often crude estimates based on domain expertise or historic data. As we enter the age of big data, large amounts of data is available and thus parameters can be estimated with greater precision. For example, ongoing promotion and current weather might influence the demand. The question that arises is whether such contextual data, together with historical data, can be used to improve decision making, i.e. solve the underlying optimisation problem more effectively.Such problems are encountered in load shifting [10], where the aim is to create an energy-aware day-head schedule based on predicted hourly energy prices.

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Revisiting the Self-adaptive Large Neighborhood Search

Thomas

Schaus

2018

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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Learning the Parameters of Global Constraints Using Branch-and-Bound

Cited by 5 publications

References 21 publications

Checking Constraint Satisfaction

Checking Constraint Satisfaction

An Investigation into Prediction + Optimisation for the Knapsack Problem

Revisiting the Self-adaptive Large Neighborhood Search

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